Equation 677 Database

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Magma a5c531c6ce18…

magma a5c531c6ce18
Size
321
Isomorphism class hash
a5c531c6ce18b309f92349edcdfa4ec3d8616528443bb4aaa8c1ef97ad1e517c
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 22:59:40
Display reorder
300,84,213,4,226,154,85,155,214,5,227,215,153,86,3,225,87,212,150,1,222,88,210,151,0,223,89,211,152,2,224,82,219,160,245,246,83,220,161,249,250,81,221,159,240,242,218,78,156,229,230,216,79,157,233,234,217,80,158,237,238,313,315,304,306,111,268,270,271,269,112,272,273,274,275,264,265,113,267,266,110,253,252,254,255,108,257,256,258,259,109,261,260,263,262,102,293,292,294,295,103,297,296,299,298,104,288,289,291,290,276,105,277,278,279,281,106,280,282,283,285,107,284,286,287,319,317,318,320,50,94,202,166,184,48,185,95,203,167,93,183,49,201,165,53,90,180,198,162,51,91,181,199,163,52,92,182,200,164,45,100,175,208,172,46,101,176,209,173,47,99,174,207,171,96,44,178,204,168,97,42,179,205,169,98,43,177,206,170,311,308,301,302,65,190,120,144,128,63,126,191,121,145,189,127,64,122,146,61,186,131,123,147,62,187,129,124,148,60,188,130,125,149,56,196,247,118,244,54,197,251,119,248,55,195,243,117,241,192,59,231,114,228,193,57,235,115,232,194,58,239,116,236,303,314,310,316,69,139,19,13,33,70,34,140,20,14,138,35,71,18,12,68,142,32,22,16,66,143,30,23,17,67,141,31,21,15,75,137,39,25,11,76,135,40,26,9,77,136,41,24,10,133,74,38,28,7,134,72,36,29,8,132,73,37,27,6,309,305,307,312 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#e1d7ea9e4f81623cd84c542145d634570787dd3fe7cd09a50189ca2a47386599, 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 22:59:41 · history