Equation 677 Database

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Magma 5fb01a0eb68a…

magma 5fb01a0eb68a
Size
321
Isomorphism class hash
5fb01a0eb68ab1e3a3480650cd4ddeafe4eaa48c982f8953ab64442a4e4fe9a2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:55:15
Display reorder
300,249,46,134,121,69,47,250,132,122,70,251,45,120,133,71,42,248,137,124,68,43,246,135,125,66,44,247,136,123,67,240,37,140,127,60,241,38,138,128,61,242,36,139,126,62,40,243,143,130,63,41,244,141,131,64,39,245,142,129,65,315,314,301,304,291,170,288,289,290,168,295,293,292,294,299,169,296,297,298,173,287,284,285,286,171,279,276,277,278,172,283,280,281,282,255,176,252,253,254,259,174,257,256,258,263,175,261,260,262,179,267,265,264,266,177,271,268,269,270,178,275,272,273,274,319,320,317,318,165,74,190,4,144,72,166,191,5,145,167,73,3,189,146,77,164,186,1,147,75,162,187,0,148,76,163,188,2,149,156,80,181,10,150,157,78,182,11,151,158,79,180,9,152,83,159,184,6,153,81,160,185,7,154,82,161,183,8,155,303,313,316,307,16,119,96,31,88,117,17,97,32,89,15,118,30,98,87,115,12,99,34,84,116,13,100,35,85,114,14,101,33,86,22,110,102,29,94,23,108,103,27,95,21,109,104,28,93,113,18,105,25,90,111,19,106,26,91,112,20,107,24,92,302,312,306,310,216,54,200,237,205,55,217,198,238,206,218,56,239,199,204,57,219,203,236,208,58,220,201,234,209,59,221,202,235,207,222,52,195,228,211,223,53,196,229,212,224,51,197,230,210,48,225,194,231,214,49,226,192,232,215,50,227,193,233,213,305,311,308,309 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#c93f531644bb5fd38eabd6a6f62492ff6d9a38e5937df79a955f96fa67b29b12, M = {60} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:55:16 · history