Equation 677 Database

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Magma c75e45a47627…

magma c75e45a47627
Size
321
Isomorphism class hash
c75e45a47627442a3db507d82a7d6ba7bf7807ef4db4843878984667d0c8d9fa
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 22:37:05
Display reorder
300,70,56,6,34,23,68,54,7,32,21,69,55,8,33,22,72,52,30,20,188,71,53,5,31,223,228,226,240,29,19,9,65,39,62,28,10,66,37,60,26,11,67,38,61,27,64,12,35,58,24,63,13,36,59,25,57,227,220,225,224,311,315,314,310,285,50,287,284,286,276,51,279,277,278,280,49,283,281,282,297,46,296,298,299,288,47,291,289,290,292,48,295,293,294,266,265,264,41,267,270,269,268,42,271,274,273,272,40,275,260,262,261,44,263,252,254,253,45,255,43,256,258,257,259,317,318,320,319,137,83,133,121,222,234,229,233,122,17,138,82,132,123,18,136,80,120,16,130,134,81,131,118,14,135,79,129,119,15,126,141,113,75,1,124,142,114,73,0,125,143,115,74,2,140,128,116,78,3,139,127,117,76,4,77,235,232,231,221,303,302,305,301,109,87,149,196,211,107,88,147,194,206,108,89,148,195,209,112,86,199,203,145,110,84,146,197,204,111,85,144,198,201,154,104,191,90,218,152,105,192,91,214,153,106,193,92,216,103,151,190,248,245,230,236,241,247,243,246,102,150,189,213,313,316,312,307,184,96,175,164,210,185,97,176,165,207,186,98,174,163,208,187,95,160,202,171,183,93,172,161,205,177,94,173,162,200,167,178,156,99,219,168,179,157,100,215,166,180,155,101,217,181,170,159,251,244,239,238,237,249,242,250,182,169,158,212,308,304,309,306 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#676093fc8b0a9c703c9b4a913f63a03a075a7ec27635c2c42c5b015ba025ae64, 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 22:37:06 · history