Equation 677 Database

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Magma 424b6434694a…

magma 424b6434694a
Size
321
Isomorphism class hash
424b6434694afc4fc9b359c45c1f46800a779aa5ac661b8659f5c3ac43967c51
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 22:44:52
Display reorder
316,245,275,256,238,119,74,24,223,120,222,73,23,220,117,71,25,221,118,72,26,274,255,244,239,125,216,22,67,123,217,20,68,124,215,21,66,219,122,19,70,273,257,237,243,218,121,18,69,43,44,42,39,40,41,46,45,290,277,278,279,302,301,304,311,293,295,281,283,61,161,83,214,62,213,162,84,210,63,165,82,211,64,163,80,212,65,164,81,60,206,75,159,280,294,282,292,59,205,76,160,208,56,77,158,209,57,78,156,207,58,79,157,38,36,37,34,35,33,29,27,31,32,30,28,310,306,307,312,148,169,145,52,146,147,53,168,260,265,261,241,167,144,150,55,264,259,262,242,166,143,149,54,138,174,51,153,139,172,49,151,140,173,50,152,266,258,240,263,171,141,48,154,170,142,47,155,95,93,94,98,96,97,100,99,287,288,286,285,305,319,303,313,284,276,291,289,109,90,106,14,110,15,89,105,236,252,248,251,16,111,92,108,17,112,91,107,113,12,104,88,253,235,250,247,114,13,103,87,11,115,101,85,10,116,102,86,234,254,249,246,130,131,129,126,127,128,136,137,134,132,133,135,309,308,300,314,186,3,200,183,201,187,184,0,199,2,185,182,6,203,189,179,4,204,190,180,5,202,188,181,272,232,267,269,271,233,268,270,198,1,175,191,8,196,177,193,9,197,178,194,7,195,176,192,224,225,226,227,228,229,230,231,298,296,297,299,317,315,318,320 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#8782a898cb34e59b9ea1a81d727d55f661339e265a029f2d4530f64cefd9daa9, 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 22:44:53 · history