Equation 677 Database

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Magma 21834897a6c3…

magma 21834897a6c3
Size
451
Isomorphism class hash
21834897a6c39e55ad2ba42d3c1a3c8dfac575491170c37e457bf05e7505cdf1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 450) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 21:17:56
Display reorder
442,440,443,444,445,446,441,447,449,448,450,311,239,163,68,90,56,170,325,339,106,312,240,164,69,91,49,171,326,340,107,241,313,165,70,84,50,172,327,341,108,314,242,166,71,85,51,174,328,342,109,307,243,159,72,86,52,173,329,343,110,103,236,308,160,65,87,53,167,330,344,104,237,309,161,66,88,54,168,323,345,238,105,310,162,67,89,55,169,324,351,8,1,14,28,10,11,7,22,380,381,373,372,374,375,376,377,378,379,390,391,383,382,384,385,386,387,388,389,401,400,393,392,394,395,396,397,398,399,410,411,403,402,404,405,406,407,408,409,420,421,413,412,414,415,416,417,418,419,429,431,430,423,422,424,425,426,427,428,359,361,360,353,352,354,355,356,357,358,371,369,370,363,362,364,365,366,367,368,434,439,435,437,438,432,433,436,139,232,82,286,120,215,253,204,272,306,140,233,81,287,121,216,254,198,273,299,234,141,83,288,122,217,255,199,274,300,142,235,35,289,123,218,256,200,267,301,135,228,36,290,124,219,257,201,268,302,303,229,136,37,283,125,220,258,202,269,304,230,137,32,284,126,213,252,203,270,231,305,138,33,285,119,214,350,348,271,12,13,16,30,18,24,29,20,335,48,101,316,118,63,176,92,77,153,336,41,102,317,111,64,177,93,78,154,42,337,95,318,112,57,178,94,79,155,338,43,96,319,113,58,179,38,80,156,331,44,97,320,114,59,180,39,73,157,158,45,332,98,321,115,60,181,40,74,151,46,333,99,322,116,61,182,34,75,47,152,334,100,315,117,62,175,346,76,0,3,4,6,15,21,26,5,265,147,246,291,134,280,183,191,227,207,266,148,247,292,127,281,184,192,221,208,149,259,248,293,128,282,185,193,222,209,260,150,249,294,129,275,186,194,223,210,261,143,250,295,130,276,187,195,224,211,212,144,262,251,296,131,277,188,196,225,205,145,263,244,297,132,278,189,197,226,146,206,264,245,298,133,279,347,190,349,9,2,17,31,19,23,27,25 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 451 = 11 + 5*88, 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#4a96f301c450255bdcad454804b8fd984646ebe41deb085f2b49e335998ba22d, M = {88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98} 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, 88): MacNeish's product over GF(8) x GF(11); GF(8) = F_2[x]/(x^3 + 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: 11.

last edited by qawbecrdtey at 2026-10-07 21:17:57 · history