Equation 677 Database

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Magma 295ec6a8dd70…

magma 295ec6a8dd70
Size
321
Isomorphism class hash
295ec6a8dd70783c4d2098a88f68fd202e107892565d5502672d4b3a4d917090
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 22:32:00
Display reorder
300,162,152,9,182,41,39,153,163,7,183,40,151,161,8,181,164,43,154,205,232,165,42,155,6,249,238,229,227,5,184,0,46,160,150,180,44,158,148,2,178,45,159,149,3,179,157,47,146,4,176,228,211,147,1,177,156,239,247,204,231,314,315,311,312,282,281,283,280,59,57,285,286,287,284,58,276,278,279,277,294,55,293,295,292,298,56,297,299,296,54,290,288,291,289,275,50,274,273,272,48,266,264,267,265,49,270,268,271,269,258,53,257,259,256,262,51,261,263,260,254,52,253,255,252,318,317,319,320,105,94,122,20,213,212,243,244,123,21,60,93,104,121,206,218,63,96,125,17,107,61,97,126,18,62,106,95,124,19,120,66,103,92,24,64,101,90,118,25,65,102,91,119,23,99,68,88,223,207,100,67,89,117,22,98,240,242,222,208,301,307,304,305,141,189,171,15,77,78,190,142,172,13,76,188,140,170,14,144,73,192,174,11,145,74,193,175,12,75,143,191,173,10,169,70,139,235,38,214,137,234,167,210,69,138,187,168,37,136,72,186,230,237,226,241,233,248,209,246,71,185,166,16,309,313,316,310,83,112,199,131,27,28,113,84,197,132,26,111,82,198,130,86,30,115,195,134,87,31,116,196,135,29,85,114,194,133,203,33,81,110,129,34,80,109,201,128,32,217,221,202,225,79,36,219,251,224,216,236,220,250,245,215,35,108,200,127,308,303,306,302 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#4f5c530836fd0cc12915654d9cb933b30b1ebf0f1cb96882ec953efd42c5ac65, 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 22:32:01 · history