Equation 677 Database

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Magma 0f3a787b9ab1…

magma 0f3a787b9ab1
Size
321
Isomorphism class hash
0f3a787b9ab19e9622f99d6da96c2b3ad376b40d0903ab918ba87c9747a8a785
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 22:50:33
Display reorder
300,146,145,144,148,149,147,151,152,150,154,155,153,266,264,265,269,267,268,272,270,271,275,273,274,227,225,226,223,224,222,218,216,217,221,219,220,33,34,35,32,30,31,24,25,26,27,28,29,104,102,103,107,105,106,99,100,101,98,96,97,304,309,305,313,52,51,53,50,48,49,57,58,59,56,54,55,79,80,78,82,83,81,77,75,76,73,74,72,92,90,91,95,93,94,87,88,89,86,84,85,43,44,42,46,47,45,41,39,40,37,38,36,71,69,70,67,68,66,62,60,61,65,63,64,317,319,318,320,278,277,276,280,281,279,283,284,282,286,287,285,235,236,234,238,239,237,233,231,232,229,230,228,162,163,164,165,166,167,160,161,159,156,157,158,116,114,115,119,117,118,111,112,113,110,108,109,7,8,6,10,11,9,5,3,4,0,2,1,303,312,308,316,173,172,171,168,169,170,178,179,177,174,175,176,12,13,14,15,16,17,18,19,20,21,22,23,290,288,289,293,291,292,296,294,295,299,297,298,127,128,126,130,131,129,125,123,124,121,122,120,245,243,244,241,242,240,251,249,250,247,248,246,301,311,306,314,263,262,261,258,259,260,253,254,252,256,257,255,183,184,185,182,180,181,189,190,191,188,186,187,211,212,210,214,215,213,209,207,208,205,206,204,192,193,194,195,196,197,198,199,200,201,202,203,140,138,139,143,141,142,135,136,137,134,132,133,302,310,307,315 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {62} 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 22:50:34 · history