Equation 677 Database

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Magma 6512ae3493b8…

magma 6512ae3493b8
Size
401
Isomorphism class hash
6512ae3493b8148125c96ef6d78990e0f0509f9483b9be41e6a78897acb1cd6b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 400) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 09:06:02
Display reorder
400,334,113,335,336,337,338,339,340,359,94,95,96,89,90,91,92,93,119,120,78,79,80,74,345,75,76,77,103,104,97,98,99,100,101,102,70,71,72,344,73,67,68,69,81,82,83,84,85,86,87,88,110,111,112,105,106,107,108,109,66,59,60,61,62,63,64,65,115,116,117,118,114,369,364,374,379,384,389,394,399,143,138,144,145,146,147,148,141,142,128,129,130,131,132,133,134,347,136,137,355,307,311,315,318,322,326,330,289,290,291,292,353,286,287,288,149,150,151,152,153,154,155,156,161,162,163,164,157,158,159,160,172,165,166,167,168,169,170,171,127,121,122,123,346,124,125,126,300,303,140,135,139,367,362,372,377,382,387,392,397,297,225,298,354,305,293,294,295,296,358,309,313,317,321,325,329,333,231,232,237,238,239,240,233,234,235,236,275,276,277,278,351,272,273,274,260,350,261,262,263,257,258,259,242,243,244,245,246,247,248,241,264,265,266,267,268,269,270,271,256,249,250,251,252,253,254,255,227,228,229,230,226,368,363,373,378,383,388,393,398,180,203,173,174,175,176,177,178,179,193,194,195,188,189,190,191,192,209,210,212,213,214,215,216,301,304,211,308,312,316,320,324,328,332,357,221,222,223,224,217,218,219,220,181,182,183,348,184,185,186,187,201,202,349,196,197,198,199,200,284,285,352,279,280,281,282,283,205,206,207,208,204,366,361,371,376,381,386,391,396,39,14,40,41,42,43,36,37,38,24,25,342,26,27,21,22,23,12,13,302,18,19,20,1,0,2,299,58,51,52,53,54,55,56,57,34,35,28,29,30,31,32,33,341,9,7,8,6,4,5,3,323,327,331,356,306,310,314,319,49,50,44,45,46,47,48,343,16,17,10,11,15,365,360,370,375,380,385,390,395 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 401 = 1 + 5*80, 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#67110840a79d94d64583763d62d2d2f65ec1f4dc075016fc3fafed86c2e9823f, M = {80} 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, 80): MacNeish's product over GF(16) x GF(5); GF(16) = F_2[x]/(x^4 + 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: 1.

last edited by qawbecrdtey at 2026-10-02 09:06:02 · history