Equation 677 Database

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Magma 9ede00c8131f…

magma 9ede00c8131f
Size
321
Isomorphism class hash
9ede00c8131f682e572ba0cf23447d0384d372fd9a8a38d9b031cc1d8a7effe8
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 22:51:16
Display reorder
300,106,2,120,149,197,107,1,121,150,199,3,108,122,151,202,109,50,119,148,196,110,0,118,146,191,111,225,231,147,194,53,104,112,141,28,51,105,113,142,29,52,103,114,143,30,100,56,115,144,31,101,54,116,145,32,102,55,117,232,236,314,309,312,305,291,247,288,289,290,295,248,292,293,294,246,299,297,296,298,287,250,285,284,286,279,251,276,277,278,283,249,281,280,282,245,255,254,253,252,243,259,258,256,257,244,263,262,260,261,267,241,266,265,264,271,242,270,269,268,275,240,274,272,273,320,317,318,319,177,9,138,68,229,235,7,139,69,87,8,178,140,70,88,176,5,137,71,86,174,6,135,72,84,175,4,136,73,85,15,168,129,74,79,13,169,130,75,80,14,170,131,76,81,171,11,132,77,82,172,12,133,78,83,173,10,134,227,228,304,302,311,307,126,187,165,41,211,127,185,166,39,212,186,128,167,40,213,125,190,164,44,210,123,188,162,42,208,124,189,163,43,209,182,154,157,47,203,183,155,158,45,204,184,156,159,46,205,153,181,160,224,206,233,179,234,48,237,152,180,161,49,207,316,301,306,310,218,23,94,198,58,219,24,95,200,59,22,217,96,201,57,214,26,97,195,61,215,27,98,192,62,216,25,99,193,60,21,222,92,35,64,19,223,93,33,65,20,221,91,34,63,220,17,89,38,226,239,18,230,36,67,238,16,90,37,66,308,315,303,313 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#ba8e767ab0f178377cc5ca58de8baa4e7db92c571ba3737b1b055d153a9d0c2e, 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 22:51:17 · history