Equation 677 Database

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Magma c37b8ef21218…

magma c37b8ef21218
Size
321
Isomorphism class hash
c37b8ef21218690b497abb404612301e8fdc72d30d0334f007bf8b9c1441e524
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 22:22:45
Display reorder
300,144,18,104,180,203,181,19,145,102,201,182,20,146,103,202,21,183,147,107,199,184,105,22,148,200,23,185,149,106,198,186,150,16,99,194,187,151,17,100,192,188,152,15,101,193,153,189,12,98,197,154,190,13,96,195,155,191,14,97,196,306,302,308,305,299,6,296,298,297,291,7,290,289,288,294,8,295,293,292,9,283,282,280,281,286,284,10,287,285,11,278,279,277,276,263,262,4,260,261,254,255,5,252,253,259,258,3,256,257,274,275,1,272,273,266,267,0,265,264,270,271,2,269,268,319,320,318,317,74,110,69,85,179,86,108,72,70,177,84,109,73,71,178,113,88,77,68,175,89,66,111,75,176,112,87,76,67,174,91,80,116,60,170,92,78,114,61,168,90,79,115,62,169,83,94,119,63,173,81,95,117,64,171,82,93,118,65,172,304,301,316,315,35,37,226,227,167,222,38,33,223,165,224,36,34,225,166,40,218,31,219,163,221,220,41,32,164,39,216,30,217,162,209,26,43,208,158,204,24,44,205,156,206,25,42,207,157,29,215,46,214,161,27,210,47,211,159,28,212,45,213,160,310,309,307,303,250,120,49,251,143,247,121,246,50,141,249,122,248,48,142,123,243,242,52,139,245,53,124,244,140,125,241,240,51,138,232,233,126,55,134,228,229,127,56,132,230,231,128,54,133,239,238,129,58,137,234,235,130,59,135,237,236,131,57,136,312,313,314,311 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#24d4369d63c88701266d916dc6f9c75e12853e26a0a22f3b011b6cf68ccd31bb, 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 22:22:46 · history