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- W2950879073 abstract "This paper deals with combinatorial aspects of finite covers of groups by cosets or subgroups. Let $a_1G_1,...,a_kG_k$ be left cosets in a group $G$ such that ${a_iG_i}_{i=1}^k$ covers each element of $G$ at least $m$ times but none of its proper subsystems does. We show that if $G$ is cyclic, or $G$ is finite and $G_1,...,G_k$ are normal Hall subgroups of $G$, then $kgeq m+f([G:bigcap_{i=1}^kG_i])$, where $f(prod_{t=1}^r p_t^{alpha_t})=sum_{t=1}^ralpha_t(p_t-1)$ if $p_1,...,p_r$ are distinct primes and $alpha_1,...,alpha_r$ are nonnegative integers. When all the $a_i$ are the identity element of $G$ and all the $G_i$ are subnormal in $G$, we prove that there is a composition series from $bigcap_{i=1}^kG_i$ to $G$ whose factors are of prime orders. The paper also includes some other results and two challenging conjectures." @default.
- W2950879073 created "2019-06-27" @default.
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- W2950879073 date "2005-01-25" @default.
- W2950879073 modified "2023-09-27" @default.
- W2950879073 title "Finite covers of groups by cosets or subgroups" @default.
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