Equation 677 Database

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Magma 2efaa440cd55…

magma 2efaa440cd55
Size
381
Isomorphism class hash
2efaa440cd55e1f0b5e582352ad5f297991fbede795133d3948782d29453ea82
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:35:23
Display reorder
380,5,171,262,56,226,180,220,50,2,272,71,185,276,15,211,161,82,120,308,236,91,156,116,231,307,96,146,250,311,135,75,20,200,190,282,10,66,205,286,196,141,130,105,310,245,45,36,41,30,25,291,215,266,175,61,87,166,111,241,306,151,100,309,255,125,295,335,350,330,346,375,340,360,365,356,371,7,173,263,58,228,183,223,53,3,273,73,188,278,18,213,163,84,123,320,238,93,158,118,233,319,98,148,253,323,138,78,23,203,193,283,13,68,208,288,198,143,133,108,322,248,48,38,43,33,28,293,218,268,178,63,89,168,113,243,318,153,103,321,258,128,298,338,353,333,348,378,343,363,369,358,373,8,174,264,59,229,184,224,54,4,274,74,189,279,19,214,164,81,124,301,239,94,159,119,234,302,99,149,254,303,139,79,24,204,194,284,14,69,209,289,199,144,134,109,305,249,49,39,44,34,29,294,219,269,179,64,86,169,114,244,300,154,104,304,259,129,299,339,354,334,349,379,344,364,368,359,374,6,172,260,57,227,182,222,52,1,270,72,187,275,17,212,162,83,122,316,237,92,157,117,232,315,97,147,252,313,137,77,22,202,192,280,12,67,207,285,197,142,132,107,312,247,47,37,42,32,27,292,217,265,177,62,88,167,112,242,317,152,102,314,257,127,297,337,352,332,347,377,342,362,367,357,372,9,170,261,55,225,181,221,51,0,271,70,186,277,16,210,160,80,121,326,235,90,155,115,230,325,95,145,251,329,136,76,21,201,191,281,11,65,206,287,195,140,131,106,328,246,46,35,40,31,26,290,216,267,176,60,85,165,110,240,324,150,101,327,256,126,296,336,351,331,345,376,341,361,366,355,370 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#8d944e514216d4896f15b10e8d6cfc32a88a33c4742733ce5a4d2024a617afbd, M = {71} 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 23:35:24 · history