Equation 677 Database

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Magma aaebd150bac4…

magma aaebd150bac4
Size
321
Isomorphism class hash
aaebd150bac4b2bb722a403aa8f90233e78f023249136e6d0f0fe63c16460fb5
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 22:32:35
Display reorder
300,18,51,110,39,31,19,52,40,32,111,17,50,112,41,33,53,16,113,42,30,54,15,114,43,239,225,220,233,44,179,145,56,108,45,34,141,57,109,46,35,143,55,107,47,36,13,58,105,48,37,138,59,106,49,38,14,226,232,224,223,302,315,301,309,11,279,277,276,278,12,283,280,282,281,10,287,284,285,286,291,7,289,288,290,295,8,293,292,294,299,9,296,297,298,2,270,268,269,271,3,274,272,273,275,0,266,264,265,267,5,254,252,253,255,6,258,256,257,259,4,262,260,261,263,319,318,317,320,86,66,129,94,222,229,228,230,26,130,85,65,131,93,25,69,88,128,91,28,67,89,126,92,29,68,87,127,90,27,84,62,134,99,24,82,63,135,97,22,83,64,136,98,23,80,61,133,95,20,81,60,132,96,21,79,227,235,231,221,312,306,313,305,103,118,149,195,194,192,119,188,183,150,104,120,151,189,184,117,102,148,186,182,115,100,146,187,180,116,101,147,185,181,210,123,154,219,218,216,124,155,207,206,204,125,156,213,212,198,122,153,251,250,248,234,236,245,244,242,121,152,201,200,314,310,307,308,137,161,176,190,191,193,162,73,75,177,139,160,175,74,1,157,140,174,71,77,158,142,168,72,78,159,144,178,70,76,211,166,170,215,214,217,167,171,202,203,205,165,169,209,208,199,163,173,247,246,249,237,238,241,240,243,164,172,197,196,311,303,304,316 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#58222ccd0574e7adf03b9b32a848bfc3e464df8d7127a3e76f96a819fe65341a, 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 22:32:36 · history