Equation 677 Database

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Magma 4109065ce095…

magma 4109065ce095
Size
321
Isomorphism class hash
4109065ce0957701f15811e742f87cdc14a7a7c56f00dc28240439d558739dd9
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 22:22:23
Display reorder
300,176,175,174,178,179,177,173,171,172,169,170,168,140,138,139,143,141,142,135,136,137,134,132,133,152,150,151,155,153,154,147,148,149,146,144,145,164,162,163,167,165,166,159,160,161,158,156,157,35,33,34,31,32,30,26,24,25,29,27,28,303,309,315,314,262,261,263,260,258,259,252,253,254,255,256,257,267,268,269,266,264,265,273,274,275,272,270,271,280,281,279,276,277,278,286,287,285,282,283,284,292,293,291,288,289,290,298,299,297,294,295,296,249,250,251,248,246,247,240,241,242,243,244,245,317,318,319,320,55,54,56,57,58,59,52,53,51,48,49,50,61,62,60,64,65,63,67,68,66,70,71,69,73,74,72,76,77,75,79,80,78,82,83,81,44,42,43,47,45,46,39,40,41,38,36,37,184,185,183,180,181,182,190,191,189,186,187,188,316,308,304,313,21,23,22,19,20,18,14,12,13,17,15,16,91,92,90,94,95,93,89,87,88,85,86,84,103,104,102,106,107,105,101,99,100,97,98,96,115,116,114,118,119,117,113,111,112,109,110,108,192,193,194,195,196,197,198,199,200,201,202,203,302,310,305,312,1,2,0,5,3,4,8,6,7,11,9,10,211,212,210,214,215,213,209,207,208,205,206,204,223,224,222,226,227,225,221,219,220,217,218,216,235,236,234,238,239,237,233,231,232,229,230,228,126,127,128,129,130,131,124,125,123,120,121,122,301,307,306,311 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, 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 22:22:24 · history