Equation 677 Database

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Magma 4e55b2ef6c26…

magma 4e55b2ef6c26
Size
321
Isomorphism class hash
4e55b2ef6c26784cd6d9a5d87caabd26eeaf4eb8a3e3f83cd427d1a94819cdd8
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 22:50:20
Display reorder
300,76,55,153,40,181,77,53,154,38,182,78,54,152,39,180,51,79,155,208,234,52,80,156,37,248,239,212,228,36,183,74,60,151,33,179,75,58,149,31,177,73,59,150,32,178,57,72,147,35,175,210,211,148,34,176,56,241,245,207,233,311,313,315,308,21,281,280,283,282,19,284,285,287,286,20,277,276,279,278,293,24,292,295,294,296,22,297,299,298,289,23,288,291,290,27,272,273,275,274,25,264,265,267,266,26,268,269,271,270,257,30,256,259,258,261,28,260,263,262,253,29,252,255,254,317,318,319,320,47,116,84,91,218,209,244,242,92,105,46,115,85,93,217,219,50,83,94,107,118,48,81,95,108,117,49,82,96,106,43,114,88,97,104,44,112,89,98,102,45,113,90,99,103,110,42,87,213,216,111,41,86,100,101,109,238,243,214,215,310,303,304,314,8,189,142,161,170,6,190,143,162,171,7,188,141,160,169,192,4,145,164,173,193,5,146,165,174,191,3,144,163,172,11,187,140,230,168,205,185,227,158,232,10,186,139,159,167,184,2,138,229,247,235,236,226,246,231,249,9,137,157,166,309,312,316,307,64,132,123,199,18,65,133,124,197,16,66,131,122,198,17,135,63,126,195,14,136,61,127,196,15,134,62,125,194,13,69,130,121,203,0,70,129,120,201,1,71,225,222,202,204,128,68,220,251,206,224,240,221,250,237,223,67,119,200,12,301,302,306,305 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#b82bea23d952545bcb5d6b6a0cc235694bb3bc5cc3b3a153b6c38e307d02b955, 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 22:50:21 · history