Equation 677 Database

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Magma 1dad9e9d3767…

magma 1dad9e9d3767
Size
396
Isomorphism class hash
1dad9e9d3767b250bcd72382eae63f318a334f794e775514506e19687f6f3b5a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 395) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-02 05:58:11
Display reorder
377,354,335,346,353,263,336,265,239,264,149,267,240,266,150,273,241,272,151,279,242,278,152,350,343,351,344,347,153,250,154,256,243,251,155,257,244,252,156,258,245,253,157,259,246,254,158,260,247,348,337,352,345,349,159,261,248,160,255,262,249,148,140,141,142,143,144,145,146,147,331,139,332,333,334,362,388,380,378,382,319,104,111,119,80,105,120,112,82,106,121,113,64,107,122,114,65,108,123,115,66,96,124,359,361,324,67,97,68,98,125,116,69,99,327,325,316,357,328,326,317,100,271,270,72,101,277,276,74,323,360,358,76,102,117,109,103,78,118,110,46,52,53,54,55,56,57,58,45,47,48,49,50,51,314,390,375,376,384,373,365,364,175,281,211,176,196,282,212,177,197,283,0,178,198,280,222,179,199,287,223,180,200,181,201,288,225,290,203,182,202,292,204,183,189,294,205,184,190,296,206,185,191,298,207,186,192,300,208,187,193,302,209,188,194,210,304,174,195,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,385,395,394,383,356,340,309,30,91,224,31,12,268,226,32,13,274,213,21,14,320,339,355,15,83,214,22,16,23,17,84,215,85,216,24,18,86,217,25,19,321,366,310,20,87,218,26,7,88,219,27,8,89,220,28,9,90,221,29,10,367,322,311,11,235,227,228,229,230,231,232,233,234,236,237,238,341,342,368,393,391,387,386,371,338,318,127,2,171,128,79,269,172,129,81,275,173,130,59,92,161,131,60,93,162,132,61,133,62,94,163,95,164,134,63,6,165,329,315,307,363,330,306,308,166,135,70,5,167,136,71,4,168,137,73,3,169,138,75,170,1,126,77,41,33,34,35,36,37,38,39,40,42,43,44,312,313,372,381,392,379,389 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 396 = 1 + 5*79, 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#7fd9b57d9d47f149dcae21b99bbb486e9ed16acb343863fc90869d5061310077, M = {75} 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, 79): MacNeish's product over GF(79); 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: 21.

last edited by qawbecrdtey at 2026-10-02 05:58:14 · history