Equation 677 Database

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Magma 2f73bce975d9…

magma 2f73bce975d9
Size
321
Isomorphism class hash
2f73bce975d96267580907fcd1b8b7a7f6d14abd44bce12733385c3a3b746faf
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 22:21:54
Display reorder
320,245,244,246,247,108,109,99,100,101,102,103,104,105,106,107,116,117,118,119,120,248,249,250,251,110,111,112,113,114,115,121,122,123,124,125,126,127,128,129,130,254,255,252,253,136,137,138,139,140,141,142,131,132,133,134,135,289,290,291,288,302,312,305,314,285,284,286,287,94,95,96,97,98,88,89,90,91,92,93,87,75,76,77,78,79,80,81,82,83,84,85,86,282,283,280,281,59,47,48,49,50,51,52,53,54,55,56,57,74,60,61,62,63,64,65,66,67,68,69,70,71,72,73,58,308,309,306,311,28,27,29,30,31,32,33,34,236,237,238,239,35,25,26,44,240,241,242,243,45,46,36,37,38,39,40,41,42,43,19,20,21,22,23,24,232,233,234,235,15,16,17,18,3,4,5,6,7,8,9,10,11,12,13,14,276,277,278,279,315,304,307,313,293,292,294,295,167,168,169,170,171,172,173,174,262,263,264,267,175,176,177,178,179,180,181,182,183,184,185,186,265,266,260,261,166,154,155,156,157,158,159,160,161,162,163,164,256,257,258,259,147,148,149,150,151,152,153,143,144,145,146,165,300,303,301,310,200,199,201,187,188,189,190,191,192,193,194,195,196,197,198,202,203,204,205,206,207,208,209,210,271,272,273,268,269,270,274,275,228,229,230,231,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,1,0,2,298,299,297,296,317,318,319,316 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#17d8eb76b6bf5b6d0c7c94cbffab8bf30c3f61585a1079f6e7ebccc76f8bf7d1, 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 22:21:55 · history