Equation 677 Database

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Magma 951c4bc6ee69…

magma 951c4bc6ee69
Size
381
Isomorphism class hash
951c4bc6ee69cf5715b5a6f2bb95a24cf3ce338a747056032bf3fcdff8028fd3
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 23:48:17
Display reorder
380,296,286,281,271,276,265,310,311,309,307,308,306,17,18,16,20,225,19,125,131,120,140,145,135,44,45,43,47,220,46,34,35,210,31,32,33,175,165,170,161,151,156,245,236,241,260,250,255,13,14,12,42,216,15,190,185,181,200,206,196,28,27,290,231,29,26,356,360,331,341,350,335,366,345,379,371,295,285,282,270,275,266,322,323,321,319,320,318,10,11,9,21,226,8,126,130,121,141,146,136,4,5,48,7,221,6,1,36,211,3,0,2,176,166,171,160,150,155,246,235,240,261,251,256,38,39,37,41,215,40,191,186,180,201,205,195,23,22,291,230,25,24,355,361,330,340,351,336,365,346,376,370,297,287,283,272,277,267,325,326,324,328,329,327,87,88,89,90,228,91,127,134,122,142,147,137,82,83,84,85,223,86,75,76,213,72,73,74,177,167,172,162,152,157,248,238,243,263,253,258,81,78,77,80,218,79,193,188,183,203,208,198,95,94,293,233,92,93,358,362,333,343,353,338,367,348,377,372,299,289,280,274,279,269,312,313,314,315,316,317,111,112,113,114,229,115,129,133,124,144,149,139,106,107,108,109,224,110,99,100,214,96,97,98,179,169,174,164,154,159,249,239,244,264,254,259,105,102,101,104,219,103,194,189,184,204,209,199,119,118,294,234,116,117,359,364,334,344,354,339,369,349,378,374,298,288,284,273,278,268,301,300,302,303,304,305,65,66,64,68,227,67,128,132,123,143,148,138,60,61,59,63,222,62,52,53,212,49,50,51,178,168,173,163,153,158,247,237,242,262,252,257,55,56,54,58,217,57,192,187,182,202,207,197,70,69,292,232,30,71,357,363,332,342,352,337,368,347,375,373 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#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, M = {73} 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 23:48:18 · history