Equation 677 Database

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Magma 608aca5634e1…

magma 608aca5634e1
Size
321
Isomorphism class hash
608aca5634e133cd37f15f007cd2fcf056903a11ef79471392704fdf110e7660
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 22:27:43
Display reorder
311,239,268,256,275,39,148,105,223,149,222,40,106,150,42,104,220,41,151,103,221,240,269,255,274,45,146,98,216,43,147,99,217,44,145,100,215,143,47,101,219,267,241,254,273,144,46,102,218,158,159,157,154,155,156,160,161,290,288,289,291,308,301,303,318,293,294,280,276,182,205,91,33,206,29,183,92,209,181,90,31,179,207,88,32,180,208,89,30,174,211,96,38,292,295,281,277,175,210,97,37,214,176,95,34,212,177,93,35,213,178,94,36,194,195,193,197,198,196,200,201,202,203,204,199,310,307,305,315,20,191,61,71,21,192,62,72,272,248,236,246,190,23,64,73,237,271,247,249,22,189,63,74,25,184,60,75,26,185,58,76,24,186,59,77,270,238,245,250,187,28,57,78,188,27,56,79,67,65,66,70,68,69,152,153,285,286,284,287,302,319,300,316,282,283,279,278,114,140,81,54,139,55,113,80,266,258,251,244,111,142,83,53,112,141,82,52,107,138,85,49,257,265,252,242,108,137,84,48,135,109,86,51,136,110,87,50,264,259,253,243,164,162,163,167,165,166,170,168,172,173,171,169,304,306,309,317,123,0,12,129,124,2,10,130,1,128,122,11,4,119,15,125,120,5,13,126,121,3,14,127,260,232,235,262,261,233,234,263,115,6,16,134,8,117,19,131,9,118,17,132,7,116,18,133,224,225,226,227,228,229,230,231,298,296,297,299,312,314,313,320 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#38a4e23a99caaa7b44b0fde217361d7389ff59fad772c7ae239f5a60818fe03a, 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 22:27:44 · history