Equation 677 Database

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Magma 22ecb89d736d…

magma 22ecb89d736d
Size
321
Isomorphism class hash
22ecb89d736d860eb1f9cd72b4bbab467a5f2139ed4e9cb92cbc2ffbea227898
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 22:22:37
Display reorder
300,23,22,21,18,19,20,13,14,12,16,17,15,217,218,216,220,221,219,223,224,222,226,227,225,127,128,126,130,131,129,125,123,124,121,122,120,274,275,273,270,271,272,265,266,264,268,269,267,174,175,176,177,178,179,172,173,171,168,169,170,301,310,312,314,87,89,88,85,86,84,95,93,94,91,92,90,83,81,82,79,80,78,74,72,73,77,75,76,58,59,57,54,55,56,49,50,48,52,53,51,70,71,69,66,67,68,61,62,60,64,65,63,100,101,99,96,97,98,106,107,105,102,103,104,317,319,318,320,229,228,230,231,232,233,234,235,236,237,238,239,282,283,284,285,286,287,280,281,279,276,277,278,142,143,141,138,139,140,133,134,132,136,137,135,183,184,185,182,180,181,189,190,191,188,186,187,31,32,30,34,35,33,29,27,28,25,26,24,304,308,306,313,294,296,295,299,297,298,291,292,293,290,288,289,8,6,7,11,9,10,3,4,5,2,1,0,195,196,197,194,192,193,201,202,203,200,198,199,244,245,243,240,241,242,250,251,249,246,247,248,150,151,152,153,154,155,148,149,147,144,145,146,303,311,305,316,210,212,211,215,213,214,207,208,209,206,204,205,37,38,36,40,41,39,43,44,42,46,47,45,115,116,114,118,119,117,113,111,112,109,110,108,164,162,163,167,165,166,159,160,161,158,156,157,262,263,261,258,259,260,253,254,252,256,257,255,302,309,307,315 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 = {64} 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 22:22:38 · history