Equation 677 Database

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Magma 2e76d732a144…

magma 2e76d732a144
Size
321
Isomorphism class hash
2e76d732a14411b77a4a4d17e4c7583d45261cb4b16873890e770be7aeea6ded
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 22:45:14
Display reorder
300,165,142,104,178,56,166,102,179,54,143,167,141,103,177,55,138,164,107,174,59,139,162,105,175,57,140,163,106,176,58,99,133,156,169,51,100,134,157,170,52,101,132,158,168,53,136,98,159,172,50,137,96,160,173,48,171,135,97,161,49,305,308,304,309,293,295,251,294,292,296,249,298,297,299,289,291,250,290,288,279,277,247,278,276,283,280,248,282,281,287,284,246,286,285,242,259,256,258,257,240,263,261,262,260,241,255,252,254,253,271,245,268,270,269,275,243,272,274,273,266,267,244,264,265,319,317,320,318,61,12,109,24,122,62,110,25,120,13,60,14,108,26,121,15,64,112,27,125,16,65,113,28,123,17,63,111,29,124,115,18,67,30,128,116,19,68,31,126,114,20,66,32,127,21,118,70,33,131,22,119,71,34,129,35,23,117,69,130,301,302,316,315,94,190,43,144,81,95,44,145,82,191,93,189,42,146,83,186,90,46,147,80,187,91,47,148,78,188,92,45,149,79,41,181,85,150,72,39,182,86,151,73,40,180,84,152,74,184,37,88,153,75,185,38,89,154,76,155,183,36,87,77,306,310,303,307,236,201,1,237,214,238,0,239,215,202,235,203,2,234,213,200,228,3,229,210,198,231,4,230,211,199,233,5,232,212,6,192,219,218,205,7,193,221,220,206,8,194,217,216,204,195,9,224,225,208,196,10,227,226,209,223,197,11,222,207,312,314,313,311 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#9017e525a3aedea68e654a603b277c6c50731afc33f3d9497441ab6abb8d2314, 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 22:45:15 · history