Equation 677 Database

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Magma 5abe5f5791de…

magma 5abe5f5791de
Size
381
Isomorphism class hash
5abe5f5791def614ed292fe20ebbe968cb79423bb1ec042818793ad93298aeff
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:17:37
Display reorder
380,155,150,161,166,171,176,42,43,38,39,40,41,29,30,31,26,27,28,232,235,211,216,221,226,300,302,301,323,303,304,23,24,25,20,21,22,187,192,197,202,207,182,97,98,99,100,2,147,270,276,281,286,291,296,250,256,261,266,240,245,33,32,34,35,36,37,348,347,361,335,368,342,376,371,352,349,156,151,160,165,170,175,95,96,146,92,93,94,81,82,83,84,85,80,230,236,210,215,220,225,328,329,324,325,326,327,90,91,86,87,88,89,186,191,196,201,205,181,75,76,77,78,79,74,271,275,280,285,290,295,251,255,260,265,241,246,5,4,6,7,8,3,331,354,362,343,369,353,377,372,332,334,157,152,162,167,172,177,114,115,116,117,118,119,106,101,102,103,104,105,231,237,212,217,222,227,311,312,313,314,315,316,108,109,110,111,112,113,185,190,195,200,206,180,124,149,120,121,122,123,272,277,282,287,292,297,252,257,262,267,242,247,140,138,142,145,125,107,359,333,363,340,367,355,375,370,338,356,158,153,163,168,173,178,148,13,10,11,12,9,143,144,0,1,139,141,233,238,213,218,223,228,321,322,317,318,319,320,135,136,137,132,133,134,188,193,198,203,208,183,14,15,16,17,18,19,273,278,283,288,293,298,253,258,263,268,243,248,128,127,129,130,131,126,344,357,364,346,366,358,378,373,330,345,159,154,164,169,174,179,59,60,61,56,57,58,68,69,70,71,72,73,234,239,214,219,224,229,310,305,306,307,308,309,54,55,50,51,52,53,189,194,199,204,209,184,65,66,67,62,63,64,274,279,284,289,294,299,254,259,264,269,244,249,45,44,46,47,48,49,337,351,360,341,365,339,379,374,336,350 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, M = {75} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:17:37 · history