2,738 research outputs found
Coprime invariable generation and minimal-exponent groups
No full textColva Roney-Dougal acknowledges the support of EPSRC grant EP/I03582X/1.A finite group G is coprimely invariably generated if there exists a set of generators {g1,. .,gu} of G with the property that the orders |g1|,. .,|gu| are pairwise coprime and that for all x1,. .,xu∈G the set {g1x1,. .,guxu} generates G. We show that if G is coprimely invariably generated, then G can be generated with three elements, or two if G is soluble, and that G has zero presentation rank. As a corollary, we show that if G is any finite group such that no proper subgroup has the same exponent as G, then G has zero presentation rank. Furthermore, we show that every finite simple group is coprimely invariably generated by two elements, except for O8+(2) which requires three elements. Along the way, we show that for each finite simple group S, and for each partition π1,. .,πu of the primes dividing |S|, the product of the number kπi(S) of conjugacy classes of πi-elements satisfies. ∏i=1u kπi(S)≤|S|/2|OutS|.Peer reviewe
The maximal subgroups of the classical groups in dimension 13, 14 and 15
No full textOne might easily argue that the Classification of Finite Simple Groups is
one of the most important theorems of group theory. Given that any finite
group can be deconstructed into its simple composition factors, it is of great
importance to have a detailed knowledge of the structure of finite simple
groups.
One of the classes of finite groups that appear in the classification theorem
are the simple classical groups, which are matrix groups preserving
some form. This thesis will shed some new light on almost simple classical
groups in dimension 13, 14 and 15. In particular we will determine their
maximal subgroups.
We will build on the results by Bray, Holt, and Roney-Dougal who
calculated the maximal subgroups of all almost simple finite classical groups
in dimension less than 12. Furthermore, Aschbacher proved that the maximal
subgroups of almost simple classical groups lie in nine classes. The maximal
subgroups in the first eight classes, i.e. the subgroups of geometric type,
were determined by Kleidman and Liebeck for
dimension greater than 13.
Therefore this thesis concentrates on the ninth class of Aschbacher’s
Theorem. This class roughly consists of subgroups which are almost simple
modulo scalars and do not preserve a geometric structure. As our final
result we will give tables containing all maximal subgroups of almost simple
classical groups in dimension 13, 14 and 15
M. N. Roney, portrait--Photo 3
No full textHeadshot of M. N. Roney angled left wearing grey suit.Robert E. Cunningham (1906-1991) graduated from Oklahoma A&M College in 1932. Besides being a writer, Cunningham was a local photographer of Stillwater and a collector of glass plates. This collection of glass plate negatives and acetate base photographs held at the Oklahoma State University (OSU) Library Archives represents a portion of his collection amassed over the years. This memorabilia collection is historically significant in that it depicts the early history of OSU (A&M College), local history, and portraits of early residents of Stillwater. The digitization and documentation of this collection was made possible by an 2018-2019 Improving Access to Collections Grant sponsored by the Oklahoma Historical Records Advisory Board, administered by the Oklahoma Department of Libraries, and funded by the National Archives--National Historical Publications and Records Commission
M. N. Roney, portrait--Photo 5
No full textHeadshot of M. N. Roney wearing black suit smiling.Robert E. Cunningham (1906-1991) graduated from Oklahoma A&M College in 1932. Besides being a writer, Cunningham was a local photographer of Stillwater and a collector of glass plates. This collection of glass plate negatives and acetate base photographs held at the Oklahoma State University (OSU) Library Archives represents a portion of his collection amassed over the years. This memorabilia collection is historically significant in that it depicts the early history of OSU (A&M College), local history, and portraits of early residents of Stillwater. The digitization and documentation of this collection was made possible by an 2018-2019 Improving Access to Collections Grant sponsored by the Oklahoma Historical Records Advisory Board, administered by the Oklahoma Department of Libraries, and funded by the National Archives--National Historical Publications and Records Commission
M. N. Roney, portrait--Photo 1
No full textHeadshot of M. N. Roney facing right wearing grey suit.Robert E. Cunningham (1906-1991) graduated from Oklahoma A&M College in 1932. Besides being a writer, Cunningham was a local photographer of Stillwater and a collector of glass plates. This collection of glass plate negatives and acetate base photographs held at the Oklahoma State University (OSU) Library Archives represents a portion of his collection amassed over the years. This memorabilia collection is historically significant in that it depicts the early history of OSU (A&M College), local history, and portraits of early residents of Stillwater. The digitization and documentation of this collection was made possible by an 2018-2019 Improving Access to Collections Grant sponsored by the Oklahoma Historical Records Advisory Board, administered by the Oklahoma Department of Libraries, and funded by the National Archives--National Historical Publications and Records Commission
M. N. Roney, portrait--Photo 2
No full textHeadshot of M. N. Roney facing right wearing black suit.Robert E. Cunningham (1906-1991) graduated from Oklahoma A&M College in 1932. Besides being a writer, Cunningham was a local photographer of Stillwater and a collector of glass plates. This collection of glass plate negatives and acetate base photographs held at the Oklahoma State University (OSU) Library Archives represents a portion of his collection amassed over the years. This memorabilia collection is historically significant in that it depicts the early history of OSU (A&M College), local history, and portraits of early residents of Stillwater. The digitization and documentation of this collection was made possible by an 2018-2019 Improving Access to Collections Grant sponsored by the Oklahoma Historical Records Advisory Board, administered by the Oklahoma Department of Libraries, and funded by the National Archives--National Historical Publications and Records Commission
M. N. Roney, portrait--Photo 6
No full textHeadshot of M. N. Roney wearing black suit smiling widely.Robert E. Cunningham (1906-1991) graduated from Oklahoma A&M College in 1932. Besides being a writer, Cunningham was a local photographer of Stillwater and a collector of glass plates. This collection of glass plate negatives and acetate base photographs held at the Oklahoma State University (OSU) Library Archives represents a portion of his collection amassed over the years. This memorabilia collection is historically significant in that it depicts the early history of OSU (A&M College), local history, and portraits of early residents of Stillwater. The digitization and documentation of this collection was made possible by an 2018-2019 Improving Access to Collections Grant sponsored by the Oklahoma Historical Records Advisory Board, administered by the Oklahoma Department of Libraries, and funded by the National Archives--National Historical Publications and Records Commission
M. N. Roney, portrait--Photo 4
No full textHeadshot of M. N. Roney staring into camera not smiling.Robert E. Cunningham (1906-1991) graduated from Oklahoma A&M College in 1932. Besides being a writer, Cunningham was a local photographer of Stillwater and a collector of glass plates. This collection of glass plate negatives and acetate base photographs held at the Oklahoma State University (OSU) Library Archives represents a portion of his collection amassed over the years. This memorabilia collection is historically significant in that it depicts the early history of OSU (A&M College), local history, and portraits of early residents of Stillwater. The digitization and documentation of this collection was made possible by an 2018-2019 Improving Access to Collections Grant sponsored by the Oklahoma Historical Records Advisory Board, administered by the Oklahoma Department of Libraries, and funded by the National Archives--National Historical Publications and Records Commission
M. N. Roney, portrait--Photo 7
No full textHeadshot of M. N. Roney in grey suit looking off to right.Robert E. Cunningham (1906-1991) graduated from Oklahoma A&M College in 1932. Besides being a writer, Cunningham was a local photographer of Stillwater and a collector of glass plates. This collection of glass plate negatives and acetate base photographs held at the Oklahoma State University (OSU) Library Archives represents a portion of his collection amassed over the years. This memorabilia collection is historically significant in that it depicts the early history of OSU (A&M College), local history, and portraits of early residents of Stillwater. The digitization and documentation of this collection was made possible by an 2018-2019 Improving Access to Collections Grant sponsored by the Oklahoma Historical Records Advisory Board, administered by the Oklahoma Department of Libraries, and funded by the National Archives--National Historical Publications and Records Commission
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