153 citations · 433 across the 29 of their papers we have counts for
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Infinitely many finite simple groups of Lie type are not generated invariably by two elements of prime order
Robert M. Guralnick, John Shareshian, Russ Woodroofe
We show that there are infinitely many k for which Sp_{2k}(2) is not generated invariably by two elements of prime order.
Invariable generation of finite simple groups and rational homology of coset posets
Robert M. Guralnick, John Shareshian, Russ Woodroofe
We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary fin…
On invariable generation of alternating groups by elements of prime and prime power order
Robert M. Guralnick, John Shareshian, Russ Woodroofe
We verify that every alternating group of degree at most one quadrillion is invariably generated by an element of prime order together with an element of prime power order.
A new subgroup lattice characterization of finite solvable groups
John Shareshian, Russ Woodroofe
We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite gr…
Shelling the Coset Poset
Russ Woodroofe
It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen-M…