Equation 677 Database

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Magma 2577c4e65033…

magma 2577c4e65033
Size
321
Isomorphism class hash
2577c4e650337a71dc5a150d640f0acd553a14a8befd6039d0b1651d5bb3e028
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 22:22:41
Display reorder
300,233,107,29,90,251,27,231,91,249,105,28,232,106,92,250,25,229,103,93,247,26,230,104,94,248,228,24,102,95,246,35,239,98,88,242,237,96,89,33,240,97,238,87,34,241,101,235,84,31,245,99,236,85,32,243,100,234,86,30,244,313,315,301,303,299,298,62,297,296,60,291,288,289,290,61,295,294,293,292,65,283,282,281,280,63,287,286,285,284,279,64,278,277,276,68,263,262,261,260,255,254,253,66,252,258,259,257,67,256,274,275,272,71,273,266,267,265,69,264,270,271,268,70,269,319,317,318,320,227,209,8,167,149,6,225,165,147,207,7,226,208,166,148,11,223,205,163,145,9,224,206,164,146,222,10,204,162,144,3,218,215,158,155,216,213,156,4,153,214,217,157,5,154,211,221,161,2,151,212,219,159,1,152,210,220,160,0,150,311,302,308,316,21,39,79,142,203,80,22,143,201,40,78,23,41,141,202,82,20,38,138,199,83,18,36,139,200,19,81,37,140,198,77,12,45,133,194,13,46,134,75,192,47,14,132,76,193,44,15,136,73,197,42,16,137,74,195,43,17,135,72,196,312,307,310,305,173,130,58,114,191,59,171,115,189,131,57,172,129,116,190,54,169,126,117,187,55,170,127,118,188,168,56,128,119,186,49,179,121,112,182,177,122,113,50,180,120,178,111,48,181,124,175,108,52,185,125,176,109,53,183,123,174,110,51,184,314,306,304,309 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#24594adec9458e953c3b7e97dafa6bb51a67ac64efb5ebe0d91d39b768cf806c, 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 22:22:42 · history