Equation 677 Database

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Magma 9692c1f10865…

magma 9692c1f10865
Size
321
Isomorphism class hash
9692c1f10865030df32931df1a162d95d1eaa393b69279ecaf0bd9531323ef11
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 23:04:16
Display reorder
300,9,237,238,143,124,230,229,141,10,125,11,233,234,142,123,221,8,222,139,120,224,6,226,140,121,217,7,218,138,122,212,36,134,1,130,210,37,132,0,131,211,38,133,2,129,39,215,137,3,126,40,213,135,4,127,41,214,136,5,128,308,302,313,315,240,298,299,297,296,290,291,289,241,288,242,295,294,293,292,282,243,283,281,280,286,244,287,285,284,278,245,279,277,276,263,262,261,246,260,254,255,253,247,252,259,258,257,248,256,275,274,272,249,273,266,267,264,250,265,271,270,268,251,269,318,317,320,319,44,209,92,83,74,90,207,81,42,72,43,208,91,82,73,205,47,95,79,77,206,45,93,80,75,204,46,94,78,76,98,200,89,50,69,96,198,87,48,70,97,199,88,49,71,203,101,85,53,68,201,99,86,51,66,202,100,84,52,67,306,301,311,304,29,113,236,161,239,228,111,159,27,231,28,112,232,160,235,109,25,220,157,223,110,26,225,158,227,108,24,216,156,219,117,104,152,35,144,118,102,150,33,145,119,103,151,34,146,107,116,155,31,147,105,114,153,32,148,106,115,154,30,149,309,316,307,314,63,174,171,21,197,172,175,22,64,195,65,176,173,23,196,177,62,170,20,193,178,60,168,18,194,179,61,169,19,192,162,180,12,54,188,163,181,13,55,186,164,182,14,56,187,183,165,15,57,191,184,166,16,58,189,185,167,17,59,190,305,310,303,312 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#f6b6fc56ae6a00548325e9d66bb78aa16bb0852529ebdb9883eeafc26b8a7eae, 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 23:04:17 · history