Equation 677 Database

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Magma a2d9af279f54…

magma a2d9af279f54
Size
381
Isomorphism class hash
a2d9af279f541c7b8f2272afa79bda164cdd7ee9c1a3c4fa5388e8e560111c86
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 23:26:57
Display reorder
380,158,153,163,168,173,178,288,293,298,273,278,283,104,105,106,107,102,103,188,193,198,203,208,183,90,91,92,93,94,95,113,108,109,110,111,112,115,116,117,118,119,114,97,98,99,100,101,96,304,305,301,300,302,303,238,213,218,223,228,233,263,258,268,243,248,253,360,368,373,349,378,332,345,351,359,350,156,151,161,165,170,175,286,291,296,270,276,281,147,148,149,144,145,146,185,190,195,201,206,180,134,135,136,137,132,133,124,125,120,121,122,123,128,129,130,131,126,127,142,143,138,139,140,141,315,316,311,312,313,314,236,210,215,220,226,231,261,256,266,240,245,250,362,365,372,353,376,354,352,330,356,334,157,152,162,167,172,177,287,292,297,272,277,282,45,46,47,42,43,44,187,192,197,202,207,182,58,59,54,55,56,57,52,53,48,49,50,51,1,0,2,3,4,5,40,41,36,37,38,39,307,308,309,310,306,329,237,212,217,222,227,232,262,257,267,242,247,252,363,366,370,344,377,337,342,333,357,343,155,150,160,166,171,176,285,290,295,271,275,280,80,81,82,83,78,79,186,191,196,200,205,181,63,64,65,60,61,62,89,84,85,86,87,88,70,71,66,67,68,69,73,74,75,76,77,72,328,323,324,325,326,327,235,211,216,221,225,230,260,255,265,241,246,251,361,367,371,347,375,331,335,348,358,346,159,154,164,169,174,179,289,294,299,274,279,284,34,35,30,31,32,33,189,194,199,204,209,184,24,25,26,27,28,29,17,12,13,14,15,16,19,20,21,22,23,18,9,10,11,6,7,8,319,320,321,322,317,318,239,214,219,224,229,234,264,259,269,244,249,254,364,369,374,339,379,340,336,338,355,341 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, 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 23:26:57 · history