Equation 677 Database

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Magma 5667e55fc6c1…

magma 5667e55fc6c1
Size
321
Isomorphism class hash
5667e55fc6c1b29ff17cb55d65bbfecebc784fccdd53b0181cac1be635248c87
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 22:59:14
Display reorder
300,140,20,219,159,149,138,18,220,160,147,139,19,221,161,148,143,23,158,145,218,141,216,21,156,146,22,217,142,157,144,15,225,165,135,155,16,226,166,136,153,17,227,167,137,154,14,224,164,134,151,222,12,162,132,152,133,223,13,163,150,315,316,301,302,264,70,265,267,266,269,71,268,271,270,273,69,272,274,275,261,66,263,262,260,253,252,67,255,254,68,256,257,259,258,61,289,291,288,290,62,293,295,292,294,60,297,299,296,298,64,285,287,284,286,277,65,279,276,278,280,281,63,283,282,319,320,318,317,234,89,235,74,26,237,87,236,72,24,239,88,238,73,25,232,85,77,29,233,229,228,86,75,27,84,230,231,76,28,95,247,80,246,32,93,249,78,248,30,94,251,79,250,31,91,245,83,244,35,241,92,81,240,33,242,243,90,82,34,309,310,308,307,188,124,53,6,195,186,125,51,7,196,187,123,52,8,197,191,120,9,194,49,189,50,121,10,192,122,48,190,11,193,130,59,4,183,201,131,57,5,184,202,129,58,3,185,203,126,55,1,182,200,56,127,0,180,198,181,54,128,2,199,311,312,303,306,45,174,110,207,103,46,175,108,208,104,47,176,109,209,102,44,177,206,106,113,42,111,178,204,107,179,112,43,205,105,172,116,213,36,101,173,114,214,37,99,171,115,215,38,100,168,119,212,39,97,117,169,210,40,98,41,118,170,211,96,313,314,305,304 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#dc2fe3473be348561d898626a2f45bbebd7964bafd5487f2fff34f8adc67b3cf, 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 22:59:15 · history