Equation 677 Database

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Magma 955fdcf1b386…

magma 955fdcf1b386
Size
321
Isomorphism class hash
955fdcf1b38661420f0067acc2d82e4e4af1c4c5e505ee9a4ad4e6b4bfba02ac
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 23:04:31
Display reorder
300,158,183,52,94,59,159,60,184,50,92,157,58,182,51,93,56,155,181,55,91,57,156,186,53,228,224,234,236,54,90,64,150,177,47,87,65,151,178,48,85,63,149,176,49,86,153,61,179,46,89,154,62,180,45,88,152,225,235,223,227,309,308,313,303,39,282,283,280,281,40,285,286,287,284,41,277,278,279,276,293,42,295,294,292,297,43,299,298,296,288,44,290,291,289,273,37,275,274,272,264,38,266,267,265,269,36,270,271,268,33,256,259,258,257,34,260,262,263,261,35,252,254,255,253,320,318,317,319,83,134,101,24,248,226,241,232,102,22,84,126,133,100,23,208,82,136,104,27,216,80,137,105,25,127,81,135,103,26,125,74,132,99,30,123,75,130,97,28,124,76,131,98,29,77,121,128,95,32,78,122,129,96,31,79,230,231,229,222,310,301,311,306,107,9,70,163,193,108,194,10,71,164,106,192,8,72,165,196,110,12,69,162,197,111,13,67,160,195,109,11,68,161,191,210,15,214,217,189,213,16,114,167,190,112,14,206,211,113,188,18,245,249,247,237,220,238,242,240,187,17,66,166,302,316,304,315,203,144,171,116,5,201,3,145,172,117,202,4,143,170,115,0,199,147,174,119,185,200,148,175,120,2,198,146,173,118,21,212,142,218,215,19,219,140,169,1,20,205,141,209,207,204,7,139,250,246,251,221,233,243,239,244,6,138,168,73,305,312,307,314 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#fba993da3569b4910e46b63a02193464b761c68efe01dd1a285b47fabe43afe4, 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 23:04:32 · history