Equation 677 Database

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Magma 23453f1d8f14…

magma 23453f1d8f14
Size
321
Isomorphism class hash
23453f1d8f14ce9216781ee10ddba5be827f15552b090e10eb6d5f7cf157c72f
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 22:21:30
Display reorder
300,86,52,155,121,62,84,63,53,156,122,54,64,85,154,120,61,82,51,158,124,60,83,50,159,232,227,229,225,157,123,45,78,55,153,119,46,76,56,151,117,47,77,57,152,118,81,48,58,149,115,79,49,59,150,116,80,224,226,235,231,305,301,308,314,35,282,280,283,281,33,285,286,284,287,278,276,34,277,279,292,38,294,293,295,297,36,298,296,299,288,37,290,289,291,275,41,273,272,274,267,39,264,265,266,271,40,268,269,270,44,259,257,256,258,42,263,260,261,262,43,255,253,252,254,320,317,318,319,74,7,144,92,248,228,241,221,145,93,6,130,75,143,94,206,73,10,147,95,215,71,8,148,96,131,72,9,146,97,2,65,127,142,90,1,66,128,140,91,3,67,129,141,89,68,4,126,138,87,69,5,125,139,88,70,220,233,234,230,304,310,302,311,108,174,163,100,193,109,194,175,164,98,173,192,107,162,99,196,111,177,166,103,197,112,178,167,101,195,110,176,165,102,172,211,191,217,213,170,214,189,161,104,171,106,190,208,210,0,169,188,249,246,245,236,237,242,239,238,168,187,160,105,306,316,309,315,203,31,133,182,19,201,20,32,134,183,30,21,202,132,181,18,199,27,136,185,16,200,28,137,186,17,198,29,135,184,23,212,11,216,218,24,219,12,113,180,22,205,13,207,209,204,26,14,247,250,251,223,222,240,243,244,25,15,114,179,303,312,313,307 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#0f0ec421cc32f9c063215c008f5f1d2db6033828d1c93d9b7da541d2d3cf51f3, 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 22:21:31 · history