Equation 677 Database

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Magma 4bfb78df066e…

magma 4bfb78df066e
Size
396
Isomorphism class hash
4bfb78df066e05512005d078369903ac13657f9a004578dc3041c388ef968141
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:56:33
Display reorder
394,367,327,351,310,85,324,187,72,86,126,188,73,87,127,189,74,88,128,190,75,89,129,334,311,314,325,335,76,90,130,191,77,91,131,192,78,81,132,193,79,82,133,194,80,83,134,195,69,312,326,336,309,313,135,196,70,84,136,197,71,121,123,124,125,116,117,118,119,120,320,122,321,322,323,356,385,390,384,388,330,15,247,240,150,16,248,241,151,17,249,242,152,18,250,243,153,19,251,244,154,20,252,363,357,307,253,234,155,21,254,235,149,14,343,341,350,366,344,342,331,22,255,236,156,23,256,237,157,308,364,362,158,24,245,238,159,25,246,239,1,3,4,5,6,7,8,9,10,11,12,13,0,2,306,380,379,393,386,373,354,355,32,281,43,59,33,282,44,60,34,283,45,61,35,280,46,62,36,287,47,63,37,288,48,64,38,290,49,65,39,292,50,66,40,294,51,67,26,296,52,68,27,298,53,55,28,300,54,56,29,302,42,57,30,304,41,58,31,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,395,376,381,382,360,318,347,172,223,108,266,173,224,109,267,174,225,110,257,160,340,319,365,161,226,111,258,162,227,112,259,163,228,113,260,164,229,114,261,165,353,368,345,166,230,115,262,167,231,105,263,168,232,106,264,169,233,107,265,170,361,317,346,171,186,178,179,180,181,182,183,184,185,175,176,177,332,333,358,383,378,391,387,372,337,352,97,268,209,211,98,269,210,212,99,270,198,213,100,271,199,214,101,272,200,215,102,273,201,216,103,274,202,217,104,275,203,338,316,348,359,339,315,349,204,218,92,276,205,219,93,277,206,220,94,278,207,221,95,279,208,222,96,137,142,143,144,145,146,147,148,138,139,140,141,328,329,371,377,389,375,392 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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#0998765ec1482be10f1d3ba0fd5c4e73adbfa919f225aca7155f0867dcd51bc9, 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, 79): MacNeish's product over GF(79); 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: 21.

last edited by qawbecrdtey at 2026-10-01 23:56:34 · history