Equation 677 Database

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Magma 5b68aff503f8…

magma 5b68aff503f8
Size
381
Isomorphism class hash
5b68aff503f81844294e0c39f89fefab1f92a14f465ddbc026e68677752561c3
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:17:14
Display reorder
380,260,211,11,61,111,161,77,127,177,227,277,27,282,32,82,132,182,232,50,100,150,202,250,0,12,62,112,162,212,261,163,213,262,13,63,113,137,187,237,287,37,87,247,297,47,97,147,192,42,92,142,197,242,292,324,325,326,327,328,323,214,164,263,14,64,114,371,335,349,375,354,359,355,368,353,347,255,206,6,56,106,156,75,126,176,226,276,25,281,31,81,131,181,231,59,109,159,209,258,9,7,57,107,157,207,256,158,208,257,8,58,108,135,185,235,285,35,85,246,296,46,95,146,191,41,91,141,196,241,291,307,308,309,310,311,306,210,160,259,10,60,110,374,350,344,376,352,333,334,365,351,339,269,201,1,51,101,151,76,125,175,225,275,26,280,30,80,130,180,230,54,104,154,204,253,4,2,52,102,152,200,251,153,203,252,3,53,103,136,186,236,286,36,86,245,295,45,96,145,190,40,90,140,195,240,290,302,303,304,305,301,300,205,155,254,5,55,105,370,332,358,377,348,342,336,367,337,338,264,215,15,65,115,165,78,128,178,228,278,28,283,33,83,133,183,233,68,118,168,218,267,18,16,66,116,166,216,265,167,217,266,17,67,117,138,188,238,289,38,88,248,298,48,98,148,193,43,93,143,198,243,293,317,318,319,320,321,322,219,169,268,19,69,119,372,356,331,378,357,345,343,366,346,340,271,221,21,71,121,171,79,129,179,229,279,29,284,34,84,134,184,234,73,123,173,223,273,23,20,70,120,170,220,270,172,222,272,22,72,122,139,189,239,288,39,89,249,299,49,99,149,194,44,94,144,199,244,294,313,314,315,312,329,316,224,174,274,24,74,124,373,330,364,379,361,363,341,369,362,360 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, M = {73} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:17:20 · history