Equation 677 Database

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Magma cf1b9307871b…

magma cf1b9307871b
Size
381
Isomorphism class hash
cf1b9307871b811e3924f6b7dcb3b44dce6d96a447fd96985dc5b1012dd635e2
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 23:48:37
Display reorder
380,170,166,175,151,156,161,14,15,16,17,12,13,202,207,182,187,192,197,56,30,35,40,45,50,122,127,132,137,142,147,305,301,300,302,303,304,282,287,292,297,272,277,77,82,87,62,67,72,107,112,117,92,97,102,210,220,225,236,230,215,256,261,266,240,246,251,341,373,342,349,378,344,356,338,366,363,174,169,179,154,159,164,25,26,27,28,29,24,204,209,184,189,194,199,59,34,39,44,49,54,124,129,134,139,144,149,321,322,324,326,328,319,283,289,294,299,274,279,79,84,89,64,69,74,109,114,119,94,99,104,214,224,229,239,234,219,259,264,269,244,249,254,332,371,354,336,375,353,358,330,365,360,171,165,176,150,155,160,6,7,8,9,10,11,201,206,180,185,190,195,57,32,37,42,47,52,121,125,130,135,140,145,308,309,310,311,306,307,281,286,291,295,271,276,76,81,85,61,66,71,106,110,115,91,96,101,212,222,227,237,232,217,255,260,265,241,245,250,337,370,335,340,376,339,355,345,369,362,172,167,177,152,157,162,5,1,0,2,3,4,200,205,181,186,191,196,55,31,36,41,46,51,120,126,131,136,141,146,320,323,325,327,329,318,280,285,290,296,270,275,75,80,86,60,65,70,105,111,116,90,95,100,211,221,226,235,231,216,257,262,267,242,247,252,346,372,347,348,377,333,359,343,368,361,173,168,178,153,158,163,20,21,22,23,18,19,203,208,183,188,193,198,58,33,38,43,48,53,123,128,133,138,143,148,317,312,313,314,315,316,284,288,293,298,273,278,78,83,88,63,68,73,108,113,118,93,98,103,213,223,228,238,233,218,258,263,268,243,248,253,350,374,351,352,379,331,357,334,367,364 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 = {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 23:48:38 · history