Equation 677 Database

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Magma a2ae7641bf15…

magma a2ae7641bf15
Size
381
Isomorphism class hash
a2ae7641bf155dd0881dd8e1986990f5eb0023f518fa67931c2cc5d75319b8bb
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 23:37:34
Display reorder
380,37,42,272,57,47,52,177,182,187,192,197,202,13,17,267,28,33,22,295,155,150,165,170,162,112,117,122,127,287,132,77,277,82,62,67,72,147,137,142,292,5,4,219,208,214,234,223,229,97,87,92,282,102,107,325,326,324,328,329,327,258,253,263,237,243,248,332,357,347,337,372,365,342,362,352,379,39,44,274,59,49,54,178,183,188,193,198,203,12,19,269,27,32,20,299,157,152,167,172,160,113,118,123,128,288,133,79,279,84,64,69,74,148,138,143,293,6,7,218,207,213,233,222,228,99,89,94,284,104,109,301,300,302,303,304,305,255,251,260,239,242,245,334,358,349,339,374,367,344,363,354,377,36,41,270,56,45,50,175,180,185,191,195,200,11,16,266,25,30,21,298,159,154,169,174,164,114,119,124,129,289,134,75,276,80,60,66,71,149,139,144,294,8,9,217,206,211,231,221,226,95,86,90,280,101,106,316,317,315,313,314,312,257,252,262,236,244,247,331,359,346,336,370,369,340,364,350,375,38,43,273,58,48,53,176,181,186,190,196,201,14,18,268,29,34,23,296,156,151,166,171,161,110,115,120,126,285,130,78,278,83,63,68,73,146,136,141,291,1,0,215,205,212,230,224,225,98,88,93,283,103,108,308,306,307,311,309,310,259,254,264,238,240,249,333,355,348,338,373,366,343,361,353,376,35,40,271,55,46,51,179,184,189,194,199,204,10,15,265,26,31,24,297,158,153,168,173,163,111,116,121,125,286,131,76,275,81,61,65,70,145,135,140,290,2,3,216,209,210,232,220,227,96,85,91,281,100,105,318,319,320,321,322,323,256,250,261,235,241,246,330,356,345,335,371,368,341,360,351,378 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, M = {67} 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 23:37:35 · history