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On the finite near-rings generated by endomorphisms of an extra-special 2-group
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E. S. Garipova
Published/Copyright:
March 18, 2010
Abstract
We consider the near-rings generated by endomorphisms of some extra-special 2-groups. The most essential difference of a near-ring from a usual ring is the absence of the second distributivity. In this paper, we prove that the near-ring E(G) generated by endomorphisms of an extra-special 2-group G of order 22n+1 has the order which divides 222n+4n2 and that the near-ring E(G) of the extra-special 2-group G of type – of order 22n+1 has the order divided by 222n+4n2–2. In this case, for n = 1 and n = 2 the upper bound is attainable: the near-ring E(G) of the group D8 has the order 28, and the near-ring E(G) of an extra-special 2-group D8 * Q8 has the order 232.
Received: 2009-07-07
Published Online: 2010-03-18
Published in Print: 2010-March
© de Gruyter 2010
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Articles in the same Issue
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- On the complexity of the ℰ2 Grzegorczyk class
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- Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem
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