Equation 677 Database

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Magma 53fe2460b5e3…

magma 53fe2460b5e3
Size
321
Isomorphism class hash
53fe2460b5e3127d32c8c86484bfb7cae07fd0308550cda0db748366e5f45e29
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 22:55:18
Display reorder
300,135,24,45,59,144,133,25,43,57,145,134,26,44,58,143,61,27,137,207,228,42,136,28,60,244,236,227,210,146,41,22,39,140,54,148,23,37,138,55,149,38,21,139,56,147,142,40,19,53,150,206,205,141,52,151,20,239,243,209,229,303,306,301,316,285,286,188,287,284,276,278,189,279,277,280,282,190,283,281,299,298,296,187,297,185,288,290,291,289,294,292,295,293,186,266,179,265,267,264,270,180,269,271,268,181,274,273,275,272,261,182,262,263,260,183,254,253,255,252,258,184,256,259,257,318,319,320,317,164,166,0,113,224,208,246,237,111,120,46,162,1,112,223,220,178,176,30,123,31,168,170,114,121,174,172,115,122,29,161,33,51,108,117,159,34,49,109,118,32,160,50,110,119,47,35,157,219,222,36,158,48,107,116,156,238,240,218,221,309,310,315,313,93,198,7,13,67,91,199,8,14,65,92,197,9,15,66,16,194,96,10,70,11,94,195,17,68,196,95,18,69,12,202,5,89,234,63,235,6,215,193,212,4,201,90,192,64,88,2,200,233,241,204,251,214,247,211,249,3,87,191,62,302,304,307,305,103,165,83,163,129,101,154,81,74,127,102,155,82,75,128,175,177,106,86,132,84,104,169,167,130,173,105,171,131,85,152,78,99,203,125,153,79,100,72,126,80,232,217,73,226,98,77,231,250,225,213,245,216,248,242,230,76,97,71,124,312,311,308,314 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#cb0e3d6c08ee89c5c6b2b247efbea2db23079510829d72f3f07184542ed1a6a6, 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 22:55:22 · history