Equation 677 Database

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Magma 21e91eb3c618…

magma 21e91eb3c618
Size
321
Isomorphism class hash
21e91eb3c618fa56580dc19369e704224fb4c12acd3d8de1ba4ea43a3fdbf1e2
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 22:31:56
Display reorder
300,181,115,11,232,234,182,116,9,237,238,180,114,10,228,230,111,177,7,86,144,8,178,112,84,145,113,179,6,85,146,172,106,2,90,139,173,107,1,91,140,171,105,0,92,138,109,175,5,89,142,110,176,3,87,143,108,174,4,88,141,316,313,309,307,294,295,242,293,292,299,298,240,296,297,291,290,241,289,288,279,278,245,277,276,243,282,283,280,281,287,286,244,284,285,258,259,248,257,256,263,262,246,261,260,254,255,247,253,252,271,270,251,268,269,275,274,249,273,272,266,267,250,264,265,317,319,320,318,217,198,29,189,58,218,199,27,190,59,216,200,28,191,57,197,213,25,192,54,26,214,195,193,55,196,215,24,194,56,208,204,35,187,49,209,205,33,188,50,207,206,34,186,48,203,211,31,183,52,201,212,32,184,53,202,210,30,185,51,302,301,311,310,101,233,65,46,235,99,236,63,47,239,100,229,64,45,231,124,104,61,42,227,62,102,125,43,225,123,103,60,44,226,96,119,71,37,219,97,117,69,38,220,98,118,70,36,221,122,95,67,40,222,120,93,68,41,223,121,94,66,39,224,304,315,305,314,154,169,18,73,130,155,170,19,74,131,153,168,20,72,129,165,157,21,76,126,22,158,166,77,127,167,156,23,75,128,152,160,16,79,136,150,161,17,80,137,151,159,15,78,135,163,148,12,82,132,164,149,13,83,133,162,147,14,81,134,303,312,306,308 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#4f47b623d963c151ceba4da4fdb4170837133dc09cb743e53f258ef94ac4defc, 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 22:31:57 · history