Equation 677 Database

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Magma aa76fb3b8b63…

magma aa76fb3b8b63
Size
321
Isomorphism class hash
aa76fb3b8b630579afb5fece5c69e3042dd51b637fe4f94b673b38f02ba0cee7
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 22:59:10
Display reorder
312,234,270,258,275,8,159,108,223,7,158,109,222,5,107,160,220,6,161,221,106,233,257,271,274,216,3,163,101,217,4,164,102,2,215,162,103,219,0,166,104,273,232,272,256,218,1,165,105,197,198,199,200,201,202,203,204,293,291,292,290,300,303,301,316,280,279,288,295,86,60,190,214,87,61,191,213,85,189,64,210,83,62,211,187,84,188,63,212,206,91,58,195,294,281,278,289,92,205,59,196,208,90,57,194,209,88,55,192,207,89,56,193,35,36,34,38,39,37,41,42,43,44,45,40,310,302,307,317,81,11,70,49,82,12,71,48,252,236,248,245,80,73,10,47,251,235,244,249,79,72,9,46,54,74,15,69,52,75,16,67,76,53,17,68,246,250,237,247,51,77,13,66,50,78,14,65,184,182,183,180,181,179,186,185,284,285,286,287,309,319,308,318,283,282,276,277,155,93,19,27,154,94,18,26,269,238,253,241,157,95,29,20,156,21,96,28,31,153,97,23,242,268,254,239,152,30,98,22,32,150,99,25,33,151,100,24,243,267,255,240,172,170,171,168,169,167,178,176,173,174,175,177,305,306,304,315,114,144,126,135,115,145,124,136,116,143,125,134,117,129,140,138,118,141,139,127,119,128,142,137,264,259,265,261,263,260,266,262,113,133,149,123,131,110,146,122,132,111,147,120,130,112,148,121,224,225,226,227,228,229,230,231,298,296,297,299,313,311,314,320 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#d999f02d519da9e6482c93589338b3231f65cc1ce6e36c19968e5d782b765397, 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 22:59:11 · history