Equation 677 Database

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Magma 3157a8bab042…

magma 3157a8bab042
Size
381
Isomorphism class hash
3157a8bab042d09a70a5eedf6c59145e9f128040486bb289d9c83ba5f5233a3c
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 23:16:10
Display reorder
380,255,266,261,286,271,276,1,216,0,2,3,17,85,90,251,71,76,81,145,136,141,130,121,125,296,240,246,235,225,230,325,326,324,328,329,327,185,190,180,201,205,196,151,156,161,165,170,176,27,25,26,210,23,24,105,100,116,290,110,95,19,18,20,21,220,281,335,345,361,350,341,330,355,366,375,370,259,269,263,288,273,278,58,218,56,53,55,60,88,93,253,74,79,84,149,139,144,134,123,129,298,243,248,239,229,234,306,307,308,309,310,311,189,194,184,203,208,198,154,159,164,169,174,179,45,46,42,214,50,49,108,103,119,294,114,98,65,63,67,68,224,283,339,348,364,354,343,333,358,368,378,373,257,267,262,287,272,277,16,215,15,13,14,12,86,91,250,70,75,80,147,137,142,132,122,127,295,241,245,236,226,231,304,305,303,300,302,301,187,192,182,202,207,197,152,157,162,167,172,177,32,30,31,212,28,29,107,102,117,292,112,97,9,22,10,11,221,280,336,346,362,352,340,332,356,367,376,372,258,268,264,289,274,279,59,219,57,52,54,61,89,94,254,73,78,83,148,138,143,133,124,128,299,244,249,238,228,233,315,316,317,312,313,314,188,193,183,204,209,199,153,158,163,168,173,178,44,47,43,213,51,48,109,104,118,293,113,99,64,62,66,69,223,284,338,349,363,353,344,334,359,369,379,374,256,265,260,285,270,275,36,217,35,37,34,33,87,92,252,72,77,82,146,135,140,131,120,126,297,242,247,237,227,232,318,319,320,321,322,323,186,191,181,200,206,195,150,155,160,166,171,175,6,7,8,211,4,5,106,101,115,291,111,96,40,39,38,41,222,282,337,347,360,351,342,331,357,365,377,371 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, M = {72} 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 23:16:11 · history