Equation 677 Database

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Magma a46bde70788a…

magma a46bde70788a
Size
381
Isomorphism class hash
a46bde70788a94774c6deb908664e942d94793e2dbd16d4498cf8ce11f77c8f5
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 23:48:41
Display reorder
380,217,212,222,227,232,237,267,242,247,252,257,262,0,5,10,16,21,26,130,135,140,146,120,125,91,95,100,105,110,115,271,276,281,288,290,295,51,56,30,35,40,45,196,200,205,181,186,191,70,76,81,86,60,65,170,150,155,165,160,175,315,316,317,312,313,314,342,360,369,377,339,341,350,359,372,331,215,211,220,225,230,235,265,241,246,251,255,260,3,8,13,18,23,28,133,138,143,148,123,128,94,99,104,109,114,119,273,278,283,286,294,298,53,58,33,38,43,48,198,203,208,183,188,193,73,78,83,88,63,68,171,151,156,166,161,176,311,306,307,308,309,310,335,363,367,378,347,346,352,358,373,334,219,214,224,229,234,239,269,244,249,254,259,264,4,9,14,19,24,29,134,139,144,149,124,129,90,96,101,106,111,116,274,279,284,289,293,299,54,59,34,39,44,49,199,204,209,184,189,194,74,79,84,89,64,69,174,154,159,169,164,179,322,323,318,319,320,321,349,361,365,379,338,337,354,355,374,340,218,213,223,228,233,238,268,243,248,253,258,263,2,7,12,17,22,27,132,137,142,147,122,127,93,98,103,108,113,118,272,277,282,287,292,297,52,57,32,37,42,47,197,202,207,182,187,192,72,77,82,87,62,67,173,153,158,168,163,178,324,325,326,327,328,329,333,362,366,376,336,345,353,357,370,348,216,210,221,226,231,236,266,240,245,250,256,261,1,6,11,15,20,25,131,136,141,145,121,126,92,97,102,107,112,117,270,275,280,285,291,296,50,55,31,36,41,46,195,201,206,180,185,190,71,75,80,85,61,66,172,152,157,167,162,177,302,303,304,305,301,300,343,364,368,375,330,344,351,356,371,332 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#e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378, M = {68} 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 23:48:42 · history