Equation 677 Database

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Magma dea02aef36a4…

magma dea02aef36a4
Size
381
Isomorphism class hash
dea02aef36a49c2ca5fece7fa1b3245de9cc1e44106af6d4fdcfbb6a3f03a7ad
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 23:37:54
Display reorder
380,224,234,229,219,209,214,199,204,194,184,189,179,94,89,284,109,99,104,319,320,318,322,323,321,240,245,235,256,261,251,134,129,289,122,114,117,4,5,270,49,50,56,164,169,174,18,19,299,64,279,65,70,76,81,159,149,154,144,139,294,39,33,44,24,269,29,339,364,334,359,354,369,373,344,349,379,223,233,228,218,208,213,198,203,193,183,188,178,92,87,282,107,97,102,304,305,303,300,302,301,244,249,239,259,264,254,132,127,287,124,112,119,12,13,274,47,54,59,162,167,172,14,15,297,62,277,69,74,79,84,157,147,152,142,137,292,37,30,42,22,267,27,337,362,333,357,352,367,374,342,347,378,221,230,226,215,205,210,196,201,191,180,185,175,91,86,280,105,95,100,314,312,313,317,315,316,242,247,238,257,262,252,131,126,285,121,111,116,10,11,272,45,52,58,161,166,171,8,9,295,60,276,67,72,77,82,155,146,151,140,135,291,35,32,40,21,265,26,335,361,332,355,350,365,370,340,346,376,220,231,225,216,206,211,195,200,190,181,186,176,90,85,281,106,96,101,326,327,328,329,324,325,241,246,236,255,260,250,130,125,286,120,110,115,3,2,273,46,53,57,160,165,170,0,1,296,61,275,68,73,78,83,156,145,150,141,136,290,36,34,41,20,266,25,336,360,330,356,351,366,371,341,345,375,222,232,227,217,207,212,197,202,192,182,187,177,93,88,283,108,98,103,307,308,306,310,311,309,243,248,237,258,263,253,133,128,288,123,113,118,6,7,271,48,51,55,163,168,173,16,17,298,63,278,66,71,75,80,158,148,153,143,138,293,38,31,43,23,268,28,338,363,331,358,353,368,372,343,348,377 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 = {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 23:37:55 · history