Equation 677 Database

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Magma 76c793899af4…

magma 76c793899af4
Size
321
Isomorphism class hash
76c793899af462d916afaa654f3f59b255b9881330d299dddbbeff0b28738fa7
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 22:22:19
Display reorder
316,252,245,275,234,102,10,56,223,55,11,103,222,104,53,12,220,105,54,13,221,253,244,235,274,106,216,49,14,107,217,50,15,108,215,48,16,219,109,52,17,273,254,243,236,218,110,51,18,68,69,70,71,72,73,74,75,280,278,279,277,307,308,304,311,290,282,295,292,150,166,84,214,85,165,151,213,152,83,168,210,153,81,169,211,154,82,167,212,149,206,76,171,289,294,281,293,148,205,77,170,208,145,78,173,209,146,79,174,207,147,80,172,64,62,63,67,65,66,59,60,57,58,163,61,310,302,303,312,38,158,113,141,39,142,157,114,265,262,239,256,37,156,144,111,238,264,263,255,36,155,143,112,31,118,164,140,32,119,161,138,33,117,162,139,257,237,266,261,115,34,160,137,116,35,159,136,121,122,120,124,125,123,126,127,286,287,291,285,300,319,301,313,284,283,276,288,94,130,91,45,90,131,95,40,249,248,258,242,96,93,128,47,97,92,129,46,98,43,89,134,250,241,247,260,99,44,88,135,42,100,86,133,41,101,87,132,240,251,246,259,23,24,22,19,20,21,29,30,27,25,26,28,309,305,306,314,189,180,200,3,190,0,178,201,179,2,191,199,192,176,6,203,193,177,4,204,194,175,5,202,269,272,268,232,270,271,267,233,188,198,184,1,196,185,182,8,197,186,183,9,195,187,181,7,224,225,226,227,228,229,230,231,298,296,297,299,317,315,318,320 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#200706f015266953205238906f67170c94edeebe72a54762b43b1258f263dcc8, 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 22:22:20 · history