Equation 677 Database

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Magma cca8b1d86797…

magma cca8b1d86797
Size
396
Isomorphism class hash
cca8b1d86797c28a03a5882ee2509a1d3c786d037a73b840615ddb3d97feb770
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
2026-10-05 10:59:48
Display reorder
377,358,324,310,316,132,325,265,67,267,122,268,68,270,123,276,69,274,124,199,70,125,114,313,317,326,322,312,71,126,115,58,72,127,116,59,73,128,117,57,74,129,118,55,63,130,119,56,64,327,323,311,315,328,120,54,65,131,121,53,66,97,89,90,91,92,93,94,95,96,319,98,320,321,318,357,386,383,385,389,351,204,240,269,271,205,241,275,277,206,230,133,213,207,231,134,214,208,232,135,215,209,233,359,364,342,234,136,216,210,235,137,217,211,345,329,343,363,346,314,344,200,236,61,218,201,237,62,219,341,366,355,212,202,238,60,263,203,239,266,182,174,175,176,177,178,179,180,181,183,184,185,186,173,338,376,375,381,393,373,354,356,109,281,34,81,110,282,35,82,111,283,36,83,112,280,37,84,113,287,38,85,99,288,39,86,100,290,40,87,101,292,28,88,102,294,29,75,103,296,30,76,104,298,31,77,105,300,32,78,106,302,33,79,107,304,0,80,108,305,289,291,293,295,297,299,301,303,284,285,286,369,370,374,379,394,395,380,361,353,334,14,142,273,154,15,143,279,155,16,144,254,156,17,330,349,362,18,145,255,157,19,146,256,158,20,147,257,159,21,148,258,160,22,331,368,332,23,138,259,150,24,139,260,151,25,140,261,152,26,141,262,153,27,360,350,333,13,253,245,246,247,248,249,250,251,252,242,243,244,347,348,367,382,387,388,390,372,352,337,8,188,272,172,2,187,278,161,149,198,220,162,9,189,221,163,10,190,222,164,11,191,223,165,12,192,224,166,1,193,225,335,306,339,365,336,307,340,226,167,3,194,227,168,4,195,228,169,5,196,229,170,6,197,264,171,7,41,44,45,46,47,48,49,50,51,52,42,43,308,309,371,392,378,391,384 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#586fa5916c8de44559c4d2d7e83d13355df7bcecc9b52565b8940614810bbd71, 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 2026-10-05 10:59:48 · history